{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,25]],"date-time":"2025-11-25T17:37:15Z","timestamp":1764092235400,"version":"3.45.0"},"reference-count":36,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2025,11,23]],"date-time":"2025-11-23T00:00:00Z","timestamp":1763856000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deanship of Scientific Research at Imam Mohammad Ibn Saud Islamic University","award":["IMSIU-DDRSP2502"],"award-info":[{"award-number":["IMSIU-DDRSP2502"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This paper investigates the geometric properties of \u2217-conformal \u03b7-Ricci\u2013Yamabe solitons (\u2217-conformal \u03b7-RYS) on \u03b1-cosymplectic manifolds (\u03b1\u2212CSM) equipped with a newly introduced connection known as the generalized symmetric non-metric connection (GSNMC). The existence of this connection is rigorously established, and a thorough analysis is conducted on various curvature characteristics of \u03b1\u2212CSM manifolds in the context of the GSNMC. This paper further explores the behavior, classification, and properties of \u2217-conformal \u03b7-RYS, including their applications in different geometric settings. A particular focus is placed on the harmonic interpretation of \u2217-conformal \u03b7-RYS associated with the GSNMC on \u03b1\u2212CSM. To substantiate the theoretical developments, an explicit example is provided: a five-dimensional \u03b1-cosymplectic metric is constructed that incorporates a \u2217-conformal \u03b7-RYS structure with respect to the proposed connection. This example serves to illustrate the practical applicability of the results and validates the theoretical framework presented in the paper.<\/jats:p>","DOI":"10.3390\/axioms14120858","type":"journal-article","created":{"date-parts":[[2025,11,25]],"date-time":"2025-11-25T17:31:34Z","timestamp":1764091894000},"page":"858","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["The Generalized Symmetric Non-Metric Connection and Its Applications to \u2217-Conformal \u03b7-Ricci\u2013Yamabe Solitons on \u03b1-Cosymplectic Manifolds"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0009-0002-1727-5353","authenticated-orcid":false,"given":"Laltluangkima","family":"Chawngthu","sequence":"first","affiliation":[{"name":"Department of Mathematics and Computer Science, Mizoram University, Tanhril, Aizawl 796004, Mizoram, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6779-4883","authenticated-orcid":false,"given":"Rajesh","family":"Kumar","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Pachhunga University College, Mizoram University, Aizawl 796001, Mizoram, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5054-8865","authenticated-orcid":false,"given":"O\u011fuzhan","family":"Bahad\u0131r","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Sciences, Kahramanmaras Sutcu Imam University, Kahramanmaras 46100, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9343-0725","authenticated-orcid":false,"given":"Md","family":"Aquib","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, Mizoram University, Tanhril, Aizawl 796004, Mizoram, India"},{"name":"Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), P.O. Box-65892, Riyadh 11566, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,11,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1090\/conm\/071\/954419","article-title":"The ricci flow on surfaces","volume":"71","author":"Hamilton","year":"1988","journal-title":"Contemp. Math."},{"key":"ref_2","first-page":"2361","article-title":"Ricci-yamabe maps for riemannian flows and their volume variation and volume entropy","volume":"43","author":"Crasmareanu","year":"2019","journal-title":"Turk. J. Math."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"2150189","DOI":"10.1142\/S0219887821501899","article-title":"On Kenmotsu manifolds admitting \u03b7-Ricci-Yambe solitonns","volume":"18","author":"Yoldas","year":"2021","journal-title":"Int. J. Geom. Methods Mod. 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